Question

In the diagram, there are 14 cubes glued together to form a solid. Each cube has a volume of 1/8in^3. Find the surface area of the solid. (Show work)

Answer 1

Answer:

$10\dfrac{1}{2}in^{2}$

Step-by-step explanation:

If we solve for the surface area for each of the 14 cubes, we will come up with a surface area larger than the shape. The best way to go around this is to solve for each face of the shape.

The shape has a total of 42 faces.

The volume of a cube is s³, each cube is $\dfrac{1}{8}in^{3}$or can be converted to $(\dfrac{1}{2}in)^{3}$. So a single cube have edges that are $\dfrac{1}{2}in$.

The area of a single face of each cube is $(\dfrac{1}{2}in)^{2}$. We can also write this as $\dfrac{1}{4}in^{2}$.

Now that we have the area of a single face in the shape, we simply multiply the area by 42 faces.

Surface Area = $\dfrac{1}{4}in^{2}$ x 42

Surface Area = $10\dfrac{1}{2}in^{2}$